Prodvinutaya visualization

Download the dataset

data <- readRDS("C:/Users/enami/Downloads/very_low_birthweight.RDS")

Find and delete all NAs in columns

na_counts <- colSums(is.na(data))
data_nona <- data[, na_counts <= 100]

And now in rows

data_clean <- na.omit(data_nona)

Lets do the numeric variables density plots

numeric_v <- data_clean %>% select(where(is.numeric))
par(mfrow = c(3, 3)) 
for (var in names(numeric_v)) {
  plot(density(numeric_v[[var]], na.rm = TRUE),
       main = paste("Плотность для", var),
       xlab = var,
       ylab = "Плотность")
}

IQR=Q3−Q1 Нижняя:

Q1−1.5⋅IQR Верхняя:

Q3+1.5⋅IQR

remove_outlier <- function(data, var) {
  q <- quantile(data[[var]], probs = c(0.25, 0.75), na.rm = TRUE)
  iqr <- q[2] - q[1]
  lower <- q[1] - 1.5 * iqr
  upper <- q[2] + 1.5 * iqr
  data %>% filter(data[[var]] >= lower, data[[var]] <= upper)
}
####the function on top is supposed to remove outliers based on IQR
data_nooutlier <- numeric_v
for (var in names(data_nooutlier)) {
  data_nooutlier <- remove_outlier(data_nooutlier, var)
}

Lets do categorical transformation

categorical_v <- data_clean %>% select(where(is.character))
categorical_v <- categorical_v %>% mutate(across(everything(), as.factor))

Graph for two numeric..?

data_clean <- data_clean %>%
  mutate(dead = as.factor(dead), pneumo = as.factor(pneumo), inout = as.factor(inout))
ggplot(data = data_clean, aes(x = pneumo, fill = inout)) +
  geom_bar(position = "dodge", aes(y = ..count..)) +
  facet_wrap(~ dead, labeller = labeller(dead = c("0" = "Выжившие", "1" = "Умершие"))) +
  theme_minimal() +
  labs(
    title = "Распределение пневмонии по inout и статусу выживания",
    x = "Наличие пневмонии",
    y = "Количество случаев",
    fill = "In/Out"
  )

## Warning: The dot-dot notation (`..count..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(count)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Please, dont kill me but i will check normality probably

data_clean %>%
  group_by(inout) %>%
  summarise(shapiro = list(shapiro_test(lowph))) %>%
  unnest(shapiro)

## # A tibble: 2 × 4
##   inout        variable statistic       p.value
##   <fct>        <chr>        <dbl>         <dbl>
## 1 born at Duke lowph        0.965 0.00000000758
## 2 transported  lowph        0.965 0.0228

test <- wilcox_test(data_clean, lowph ~ inout)
test

## # A tibble: 1 × 7
##   .y.   group1       group2         n1    n2 statistic            p
## * <chr> <chr>        <chr>       <int> <int>     <dbl>        <dbl>
## 1 lowph born at Duke transported   448    83    25630. 0.0000000417

data_clean %>%
  ggplot(aes(x = inout, y = lowph, color = inout)) +
  geom_boxplot() +
  stat_compare_means(method = "wilcox.test", label = "p.signif")

rstatixplot

library(rstatix)
ggboxplot(data_clean, x = "inout", y = "lowph",
          color = "inout", palette = "jco") +
  stat_compare_means(method = "wilcox.test")

Значение lowPH статистически значимо отличаются внутри группы inout. Так как, группа transported имеет значимо более низкие уровни pH, то и выживаемость у них будет ожидаться ниже

datacontinuous <- data_clean %>%
  select(-c(birth, year, exit)) %>%  
  select_if(is.numeric)
cormatrix <- cor(datacontinuous, use = "complete.obs")
print(cormatrix)

##              hospstay       lowph       pltct        bwt        gest
## hospstay  1.000000000 -0.09460363 -0.05993874 -0.2315169 -0.18461328
## lowph    -0.094603635  1.00000000  0.26643681  0.3261464  0.37926758
## pltct    -0.059938743  0.26643681  1.00000000  0.2598576  0.06545086
## bwt      -0.231516924  0.32614640  0.25985757  1.0000000  0.69134598
## gest     -0.184613279  0.37926758  0.06545086  0.6913460  1.00000000
## twn       0.005945527  0.03835193 -0.01407561  0.1614821  0.17101963
## apg1     -0.065378517  0.26799978  0.28021129  0.3309873  0.25568063
## vent      0.252473223 -0.58322801 -0.27313969 -0.3825846 -0.41200521
## pda       0.202599688 -0.22489191 -0.22166244 -0.2591969 -0.29283921
## cld       0.385734403 -0.30046333 -0.18031810 -0.4552955 -0.42163729
##                   twn        apg1        vent         pda         cld
## hospstay  0.005945527 -0.06537852  0.25247322  0.20259969  0.38573440
## lowph     0.038351928  0.26799978 -0.58322801 -0.22489191 -0.30046333
## pltct    -0.014075607  0.28021129 -0.27313969 -0.22166244 -0.18031810
## bwt       0.161482147  0.33098733 -0.38258456 -0.25919691 -0.45529548
## gest      0.171019629  0.25568063 -0.41200521 -0.29283921 -0.42163729
## twn       1.000000000  0.06570395 -0.03854605  0.01447667 -0.08853468
## apg1      0.065703952  1.00000000 -0.33681567 -0.19312965 -0.26967928
## vent     -0.038546054 -0.33681567  1.00000000  0.35471303  0.48398148
## pda       0.014476666 -0.19312965  0.35471303  1.00000000  0.40233337
## cld      -0.088534685 -0.26967928  0.48398148  0.40233337  1.00000000

corrplot(cormatrix, method = "circle", type = "upper", order = "hclust", 
         col = colorRampPalette(c("darkblue", "white", "darkred"))(200), 
         tl.col = "black", tl.srt = 45)

heatmap(cormatrix, 
        col = colorRampPalette(c("blue", "white", "red"))(200),
        scale = "none",  # не масштабировать данные
        margins = c(10, 10))

Иерархическая кластеризация

distmx <- as.dist(1 - cormatrix)
hclust <- hclust(distmx, method = "ward.D2")
plot(hclust, main = "Иерархическая кластеризация", 
     xlab = "Переменные", sub = "", cex = 0.8)

Тепловая карта и дендрограмма

pheatmap(cormatrix,
         color = colorRampPalette(c("darkblue", "ivory", "darkred"))(200),
         cluster_rows = hclust,  
         cluster_cols = hclust,  
         main = "Тепловая карта и дендрограммы")

PCA Анализ

sapply(datacontinuous, range) #разброс значений перемнных отличается значительно требуется шкалирование!

##      hospstay    lowph pltct  bwt gest twn apg1 vent pda cld
## [1,]     -295 6.529999    16  400   23   0    0    0   0   0
## [2,]      797 7.549999   571 1500   36   1    9    1   1   1

pca <- prcomp(datacontinuous, scale. = TRUE)
summary(pca)

## Importance of components:
##                           PC1    PC2    PC3     PC4     PC5     PC6    PC7
## Standard deviation     1.8711 1.0815 1.0553 0.92904 0.88809 0.86784 0.8331
## Proportion of Variance 0.3501 0.1170 0.1114 0.08631 0.07887 0.07532 0.0694
## Cumulative Proportion  0.3501 0.4671 0.5784 0.66475 0.74362 0.81893 0.8883
##                            PC8     PC9    PC10
## Standard deviation     0.70031 0.60398 0.51133
## Proportion of Variance 0.04904 0.03648 0.02615
## Cumulative Proportion  0.93738 0.97385 1.00000

fviz_eig(pca, addlabels = TRUE, ylim = c(0, 100))

Интерпретация - standard deviation показывает разброс данных вокруг каждой из компонент, где это значение наибольшее (в нашем случае PC1) та компонента лучше всего и объясняет различие данных.Proportion of variance тоже показывает сколько наших данных обьясняет компонента, как и кумулятивная пропорция. В нашем случае наиболее важная компонента - первая

Biplot

data_dead <- datacontinuous  
data_dead$dead <- data_clean$dead
pca <- prcomp(datacontinuous, scale. = TRUE)
fviz_pca_biplot(pca, 
                geom.ind = "point",  
                pointshape = 21,     
                pointsize = 3,       
                fill.ind = data_dead$dead,  
                col.var = "black",  
                gradient.cols = c("darkblue", "cyan", "darkred"),  
                repel = TRUE,        
                legend.title = "Dead")

transfer to plotly

interactive biplot

data_clean$id <- seq_len(nrow(data_clean))
dataid <- data_clean %>%
  select(-c(birth, year, exit)) %>%
  select_if(is.numeric)
dataid$id <- data_clean$id  
dataid$dead <- data_clean$dead 
pca <- prcomp(dataid %>% select(-c(id, dead)), scale. = TRUE)
pca_2 <- as.data.frame(pca$x)
pca_2$id <- dataid$id  
pca_2$dead <- dataid$dead
pca_var <- as.data.frame(pca$rotation)
pca_var$varnames <- rownames(pca_var)
fig <- plot_ly() %>%
  # Добавление точек для наблюдений
  add_trace(
    data = pca_2,
    x = ~PC1, y = ~PC2,
    type = "scatter",
    mode = "markers",
    text = ~paste("ID:", id, "Dead:", dead),  
    hoverinfo = "text",
    marker = list(
      size = 10,
      color = ~dead,  
      colorscale = "RdBu",
      showscale = TRUE
    )
  ) %>%
  
  add_trace(
    data = pca_var,
    x = c(rep(0, nrow(pca_var)), pca_var$PC1 * 5),  
    y = c(rep(0, nrow(pca_var)), pca_var$PC2 * 5),
    type = "scatter",
    mode = "lines+text",
    line = list(color = "black"),
    text = c(rep("", nrow(pca_var)), pca_var$varnames),  
    textposition = "top right",
    hoverinfo = "text"
  ) %>%
  layout(
    title = "PCA Biplot (Interactive)",
    xaxis = list(title = "PC1"),
    yaxis = list(title = "PC2"),
    showlegend = FALSE
  )


fig

Мы не выявили причинно-следственной связи между выживаемостью и распределением другим данных, нам все равно нужно проводить дополнительный анализ выживаемости, метод главных компонент поможет нам лишь отобрать те данные, которые с большей вероятностью предскажут dead статус. Dead переменная также принимает только два значения 0 и 1 (нет и да), а для PCA нам нужны непрерывные переменные

UMAP

pca <- prcomp(dataid %>% select(-c(id, dead)), scale. = TRUE)
pca_d <- as.data.frame(pca$x)
pca_d$id <- dataid$id
pca_d$dead <- dataid$dead


umap <- umap(dataid %>% select(-c(id, dead)))


umap_d <- as.data.frame(umap$layout)
umap_d$id <- dataid$id
umap_d$dead <- dataid$dead


pcaplot <- ggplot(pca_d, aes(x = PC1, y = PC2, color = as.factor(dead))) +
  geom_point() +
  labs(title = "PCA ", color = "Dead") +
  theme_minimal()


umapplot <- ggplot(umap_d, aes(x = V1, y = V2, color = as.factor(dead))) +
  geom_point() +
  labs(title = "UMAP ", color = "Dead") +
  theme_minimal()

library(gridExtra)

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

grid.arrange(pcaplot, umapplot, ncol = 2)

UMAP change distance (я не поняла, нужно ли нам опять делать раскраску по переменной dead, сделала ее в прошлом примере навсякий случай, но дальше не буду)

umap_res_1 <- umap(dataid %>% select(-c(id, dead)), 
                   n_neighbors = 10, min_dist = 0.1)
umap_data_1 <- as.data.frame(umap_res_1$layout)
umap_plot_1 <- ggplot(umap_data_1, aes(x = V1, y = V2)) +
  geom_point(color = "pink") +
  labs(title = "UMAP") +
  theme_minimal()

umap_plot_1  

Результат - дата стала менее структурированной (нет четкого выделения кластеров, как в прошлых примерах). Я считаю, что это связано с тем что я уменьшила дистанцию и соседей и алгоритм теперь основывается на локальных связях между точками и старается их группировать компактно между собой, при этом мы упускаем глобальную структуру данных

Permutation task

data_clean$bwt_50 <- data_clean$bwt
num_rows <- nrow(data_clean)
num_permuted <- round(num_rows * 0.5)
perm_indices <- sample(1:num_rows, num_permuted)
data_clean$bwt_50[perm_indices] <- sample(data_clean$bwt_50[perm_indices])
data_clean$bwt_100 <- sample(data_clean$bwt)
perform_pca <- function(data, column_name) {
  data_numeric <- data %>% select(-c(birth, year, exit, column_name)) %>% select_if(is.numeric)
  pca <- prcomp(data_numeric, scale. = TRUE)
  pca_result <- summary(pca)
  return(pca_result)
}


perform_umap <- function(data, column_name) {
  data_numeric <- data %>% select(-c(birth, year, exit, column_name)) %>% select_if(is.numeric)
  umap_model <- umap(data_numeric)
  return(umap_model$layout)
}
pca_original <- perform_pca(data_clean, 'bwt')

## Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
## ℹ Please use `all_of()` or `any_of()` instead.
##   # Was:
##   data %>% select(column_name)
## 
##   # Now:
##   data %>% select(all_of(column_name))
## 
## See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

pca_original

## Importance of components:
##                           PC1    PC2     PC3    PC4     PC5    PC6     PC7
## Standard deviation     1.7859 1.1299 1.08060 1.0206 0.97193 0.9315 0.91101
## Proportion of Variance 0.2658 0.1064 0.09731 0.0868 0.07872 0.0723 0.06916
## Cumulative Proportion  0.2658 0.3722 0.46948 0.5563 0.63500 0.7073 0.77646
##                            PC8     PC9    PC10    PC11    PC12
## Standard deviation     0.84315 0.81449 0.69931 0.68132 0.59573
## Proportion of Variance 0.05924 0.05528 0.04075 0.03868 0.02957
## Cumulative Proportion  0.83571 0.89099 0.93174 0.97043 1.00000

umap_original <- perform_umap(data_clean, 'bwt')
umap_original

##            [,1]         [,2]
## 2    0.08134178 -1.966536179
## 4    1.93980803 -0.046309478
## 5   -0.78792197  3.947475861
## 7    2.84173343  1.100311245
## 10  -1.09816622  4.087933307
## 11   1.75893969  2.135278796
## 13   1.57316124  2.486712557
## 14  -0.71059838  4.110642262
## 15  -3.60873091 -2.302998087
## 16  -1.19219162  4.038703908
## 17   0.32280846  0.845107422
## 19   1.70882817  2.200318458
## 20   2.65620504  1.486608213
## 21  -3.10636731 -3.018667999
## 22   1.55525149  2.323932122
## 23   0.88482424  0.167100610
## 25   1.57228777  0.302639466
## 27  -1.09352000  3.911413993
## 28  -0.26872983  3.968739879
## 29  -3.17837834 -2.729470424
## 30   0.41320223 -1.526142809
## 31   0.14257462  4.012757768
## 32  -0.68084561  3.971331880
## 35   2.28234739  0.479797051
## 36  -3.78949781 -2.113417138
## 40  -0.71464294  3.984270457
## 41   0.15746315 -2.033397980
## 42   1.08758300  0.230774209
## 43   2.72694568  1.424104685
## 45  -3.41858695 -2.462539209
## 46   0.42461445  1.586874795
## 47  -0.46943981 -2.935400251
## 48   1.94437643 -0.084729197
## 50  -2.92595518 -2.787818795
## 51   1.48296831  0.406200707
## 53   0.47061231  0.374515407
## 54  -0.13828922  4.021913591
## 55   1.63459369  0.323319418
## 56   1.73329296  2.195746910
## 57   0.27673771  3.283292737
## 58   0.32449883 -1.860750735
## 59   0.94668629  0.902173757
## 62  -2.82316179 -2.906885404
## 65   0.06531802  3.761128526
## 66   1.62121114  2.261116786
## 67   0.01352182  3.901739048
## 68   0.79991427  0.371959971
## 69  -2.42020772 -2.957471313
## 70  -3.04719138 -3.067416593
## 72   0.18423962 -2.104755555
## 74   2.87172523  0.867179349
## 75   1.41398297  0.546055413
## 76  -1.18302060  3.974698727
## 77  -3.84034400 -2.093087420
## 78   0.55232887  1.955211828
## 80   1.47378103  2.098831438
## 81   2.68453363  0.915036406
## 82   0.09394661  3.239266313
## 83   2.28591904  0.693755399
## 84  -3.14563055 -2.562646268
## 85   0.21652240 -1.042085676
## 86   1.79427149  0.051520783
## 87   1.46887629  2.074180288
## 88  -3.80455403 -2.187913595
## 91   0.08243764 -2.135658848
## 92   0.16051648 -1.623706740
## 94   2.00887581  0.921777512
## 95  -3.01247806 -2.973014705
## 97  -1.08466037  4.007441442
## 98   0.88892340  0.162568054
## 99   2.65771953  1.433147195
## 101  0.93271430  0.828806078
## 102 -2.49786199 -2.961685832
## 103 -2.83125886 -2.863778054
## 104  2.94389638  1.157423487
## 105  2.19680980  0.059766690
## 107  1.52868523  2.338231628
## 108  0.06012182  3.894425318
## 109  1.33025439  0.945850866
## 111  0.28836703  3.290411211
## 114 -3.76393922 -1.942868238
## 115  0.58694776 -1.819891165
## 116 -0.03166899 -2.176174008
## 117 -0.62417555  4.023413212
## 118  1.70200579  0.578433194
## 119  0.63005660  1.075042399
## 120 -2.57483227 -2.865564572
## 121  0.22800217  0.575304602
## 122  0.50535111 -1.961687193
## 124  1.66298763  0.026527564
## 125 -3.15413865 -2.520265257
## 126  0.24762507  3.536646053
## 127  1.02239188  0.697180842
## 128  1.08599307  2.482018173
## 129  2.01309896  0.482226309
## 130 -2.96123173 -3.106520583
## 131 -1.26158119  3.991629569
## 132  0.08279661  0.467670260
## 133 -3.79472654 -2.158355602
## 134  0.75034081  1.267357908
## 137  2.01317935  0.340036538
## 139 -0.77063869  4.170797265
## 140 -0.11048696  3.999906727
## 141  0.29474333  0.384249768
## 143  0.37290667 -1.886177857
## 144  0.17598967 -2.326686368
## 145 -0.76101578  3.860048653
## 146 -3.10183897 -3.029863955
## 148  0.01181231  3.809615676
## 149 -0.41581837  1.427431468
## 150  0.59985434  2.101960641
## 151  0.47645286 -1.718167529
## 152  1.43773100 -0.141800979
## 153 -0.42585575 -0.332970605
## 154 -0.50343170  4.114776142
## 155  2.18652144  0.300169643
## 156  1.03907643  2.446005103
## 157  0.03447071  0.121985299
## 159  2.61197734  1.105051515
## 160 -0.26152948 -0.268353298
## 161 -0.03924953  1.660450399
## 162 -0.96707176  4.102712260
## 163 -0.39902096  1.283701448
## 164  1.10896048  2.627802307
## 165  1.91244738  1.902428909
## 166 -2.65044913 -2.426899694
## 167 -3.09845365 -2.682515390
## 168  1.96011265  0.314512418
## 169  3.26732263  1.135490520
## 170 -0.57131011 -0.381247347
## 172 -0.96654489  3.450760201
## 173  0.07899598  0.411514377
## 174 -0.16228067  3.825892977
## 176 -3.86878010 -2.031669494
## 177  1.76706067  2.051492759
## 179 -0.05615475 -0.575720151
## 180 -2.96119210 -2.677424145
## 182 -3.17670336 -2.587728404
## 183 -3.87508615 -2.056525275
## 184  0.01077409  0.578187462
## 185 -0.99508493  3.351106270
## 186  1.25780530  0.821003071
## 187 -0.43476370  3.773657577
## 188  2.06317325 -0.171808838
## 189  1.26543518  2.560885405
## 190  0.06288651 -2.542704946
## 191  1.84829939 -0.244464058
## 192 -0.58921890  4.225905860
## 193 -2.75430013  3.210909523
## 194 -3.70196031 -1.411678401
## 195 -3.78600417 -1.313642638
## 196  1.04465831 -0.195007742
## 197 -0.68350110  3.611756360
## 198  0.83433612  1.569518555
## 199 -0.44250362 -0.342339245
## 201  2.96477340  0.772056096
## 202  0.80276249  0.749031435
## 203  2.30325659  0.067705374
## 205  0.13270290 -2.287905011
## 206 -3.56161725 -1.165593438
## 207  3.11396102  0.626081313
## 208  0.96732452  2.436624900
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## 226 -0.29834984  4.261205006
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## 236 -0.78682646  3.385136692
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## 241 -0.04068378  3.830396982
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## 257  0.71108120 -2.534601666
## 259  0.40500501  2.660464115
## 260  0.96010353  1.250674785
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## 471 -0.27193251 -3.431796603
## 472 -0.73944698 -1.878525188
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## 476  1.09860318 -1.325430790
## 477  0.91542553 -3.174645658
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## 494  1.15233543 -3.118107619
## 495 -3.31044791  0.211042807
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## 501 -2.30302648  1.634601074
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## 503  3.43570587 -1.115676950
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## 505  4.55053223 -0.438908837
## 507 -2.81448390  2.471310506
## 508 -3.55588691 -0.888557710
## 509  4.60845843 -0.550306572
## 511 -3.03598856  0.431228369
## 512 -1.96672381  1.779271859
## 513  2.31201535 -1.963426400
## 514  4.66931022 -0.570203244
## 515 -2.93969935 -1.675717673
## 516  4.60593441 -0.504951885
## 517  2.35930807 -1.986610224
## 518 -3.61114954  0.024864564
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## 523 -2.24652891 -0.765776133
## 524 -1.33831802  2.490106197
## 525 -2.79179971  0.045713199
## 526  4.02692424 -0.528110091
## 527  1.99429024 -2.388005694
## 528 -3.39093493  1.887372593
## 529  0.49957990 -3.561123998
## 530  2.29587419 -2.039459475
## 531 -2.41476008 -2.148695567
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## 542 -1.29293095 -1.937613980
## 543  4.24586536 -0.660464385
## 545 -1.43572720 -2.457812831
## 546  0.95029364 -3.289551063
## 547  4.70593708 -0.537493368
## 548 -2.07546083  1.732019652
## 550 -3.00372072  1.902586920
## 551 -0.83589815 -2.041655919
## 555 -3.41578379  1.981674985
## 558  4.93541645  0.144845495
## 560 -2.32702784  2.204537372
## 561 -1.26973087 -1.792362196
## 563 -2.51412114  2.121752385
## 564 -3.62779765  0.112239069
## 566 -2.95074497  0.177557300
## 568 -3.06747936 -1.574271963
## 569 -2.13578834  1.988738604
## 571  2.35968792 -2.146219094
## 572  0.40762094 -3.645100781
## 573  2.13502045 -2.299632881
## 574  4.00951475 -0.898929518
## 575  2.18482150 -2.298902787
## 578  2.56513264 -1.943286128
## 579  4.77298879 -0.429573300
## 580  0.22066164 -3.612460939
## 581 -2.15415658  1.596906864
## 583 -2.29648459 -0.681985503
## 584 -2.62321531 -1.803706903
## 585  1.15201940 -3.217085684
## 586  5.02064781  0.330544548
## 587  5.05296402  0.065315758
## 588 -1.90912393 -2.579058609
## 590  0.13046222 -3.610176549
## 591 -2.72391575  2.373421361
## 592  2.46529126 -2.103754823
## 593 -2.42508833  2.266182819
## 594 -2.29058201  1.992346460
## 597 -1.96244379  0.928523158
## 599  0.98977677 -3.276426300
## 600 -3.61093400  0.035284204
## 601  5.11472020  0.244957426
## 602 -3.04766609  2.295061260
## 603 -2.13450850 -0.886130536
## 604  0.16377203 -3.644248958
## 605 -2.21017898  1.290865629
## 606  4.81901080 -0.373999474
## 608  2.74292804 -1.946104459
## 609  3.06827893 -1.796444538
## 610 -2.54996641  1.194117464
## 611 -1.37153883 -1.620737156
## 613 -2.51214025  1.441895091
## 615 -2.20041217  0.982255846
## 616  2.79199068 -1.988067226
## 619 -3.53728141  1.379802050
## 620 -3.50849956  0.236791919
## 622 -0.15175376 -3.602075411
## 623  1.65864009 -2.779756410
## 624 -0.91525405 -2.084320105
## 625  5.16456607  0.196806366
## 626  4.75937375 -0.114509800
## 628 -1.91975514  1.394647932
## 629  4.60005479  0.148073777
## 630 -1.17821953 -1.987595769
## 631  5.06591394  0.174524989
## 632 -2.67649195  0.156343641
## 634 -2.34735859  0.683023948
## 636 -1.55236716 -2.256721872
## 638 -3.34472374  1.933952319
## 641  4.76384363 -0.258736530
## 642  0.98997365 -3.262253346
## 643 -3.13512659  2.287265696
## 647 -3.67013157  0.776133282
## 648  4.16916100 -0.810442276
## 649 -1.30030611 -1.592817346
## 650  2.42829186 -2.079432257
## 652 -3.36543299  1.954875326
## 661  0.45898871 -3.624186933
## 662 -0.18321270 -3.536328869
## 664 -2.06415972  1.054689436
## 666  5.12052879  0.141230610
## 667 -2.95207029  0.003462019
## 671 -1.87076897 -1.144009841

pca_50 <- perform_pca(data_clean, 'bwt_50')
pca_50

## Importance of components:
##                          PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.872 1.1180 1.08045 1.03080 0.97266 0.91613 0.87923
## Proportion of Variance 0.292 0.1042 0.09728 0.08855 0.07884 0.06994 0.06442
## Cumulative Proportion  0.292 0.3962 0.49346 0.58200 0.66084 0.73078 0.79520
##                            PC8    PC9    PC10    PC11    PC12
## Standard deviation     0.83167 0.8154 0.69811 0.59576 0.50871
## Proportion of Variance 0.05764 0.0554 0.04061 0.02958 0.02157
## Cumulative Proportion  0.85284 0.9082 0.94886 0.97843 1.00000

umap_50 <- perform_umap(data_clean, 'bwt_50')
umap_50

##             [,1]         [,2]
## 2   -2.805938202 -4.142778707
## 4   -1.659734472  1.843844665
## 5    1.651896028  2.980084361
## 7   -0.865696963  3.598541511
## 10  -1.474080734  2.997435858
## 11  -1.172261043  3.408604910
## 13   0.402465355  3.372756309
## 14  -0.275216531  3.770191186
## 15   2.087477431 -2.024186979
## 16   2.324783927  1.590940910
## 17  -1.697844899  1.796736535
## 19  -1.334591829  3.334948627
## 20  -1.159795953  3.507331337
## 21   1.969863662 -2.293906765
## 22   0.316800868  3.339552276
## 23   2.718916658  1.144829613
## 25  -0.345329321  2.316177128
## 27   2.234690802  1.682644255
## 28   1.838435933  2.733504612
## 29  -2.577656852 -4.422138464
## 30   1.221999817 -1.581800069
## 31   1.742411745  3.215351921
## 32   1.826787028  2.731842378
## 35  -1.588236489  2.464588774
## 36  -2.873986835 -4.142412157
## 40   2.087596848  1.966540846
## 41  -2.834367268 -4.245508804
## 42  -1.109901186  1.858200160
## 43  -1.199322054  3.538077448
## 45   2.386089353 -2.420855177
## 46  -0.069705466  2.528045225
## 47  -2.175416854 -4.469870164
## 48  -1.692575581  1.730015852
## 50   2.669272369 -2.499140629
## 51  -1.585706595  1.949878307
## 53  -0.926664821  1.679694954
## 54   1.857899087  3.076089488
## 55   2.240399349  1.322876638
## 56  -1.490112374  3.496282748
## 57   1.221906735  3.068318638
## 58  -2.910578870 -4.125897565
## 59  -0.576643959  2.389942832
## 62  -2.573042373 -4.396853675
## 65   1.471552305  3.178802854
## 66   1.519447052  3.084232455
## 67   1.945670291  2.614861845
## 68  -1.152230492  1.870442601
## 69  -2.502134460 -4.255889384
## 70   1.924935434 -2.272996532
## 72  -2.953665534 -4.209753494
## 74  -2.841543175  2.572818881
## 75  -1.044015997  2.211991481
## 76  -0.301479360  2.374316564
## 77   2.930576022 -1.726766901
## 78   2.023568178  2.443847940
## 80  -1.445633111  3.150523537
## 81  -1.567114406  3.203977889
## 82   2.111757359  1.575873080
## 83  -0.852748063  2.651762071
## 84   2.929206999 -2.367507817
## 85   0.317453105 -1.847615616
## 86  -1.404280613  1.828975553
## 87   0.001821905  3.032951461
## 88   3.095806919 -1.862155564
## 91   1.832226936 -2.304528466
## 92  -2.519012589 -3.780596541
## 94   1.512120683  2.846206840
## 95  -2.639559490 -4.418329335
## 97  -1.467399069  2.763777447
## 98  -1.715433624  1.782893200
## 99  -0.162496814  3.351465942
## 101  2.189737144  1.461414737
## 102 -2.593618515 -4.335959037
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## 667  3.374602342 -0.594264695
## 671 -1.296840102 -2.488335138

pca_100 <- perform_pca(data_clean, 'bwt_100')
pca_100

## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5     PC6     PC7
## Standard deviation     1.9254 1.1503 1.07384 1.02810 0.95159 0.92141 0.84454
## Proportion of Variance 0.3089 0.1103 0.09609 0.08808 0.07546 0.07075 0.05944
## Cumulative Proportion  0.3089 0.4192 0.51530 0.60339 0.67884 0.74959 0.80903
##                            PC8     PC9    PC10    PC11    PC12
## Standard deviation     0.81575 0.73003 0.69914 0.59720 0.49779
## Proportion of Variance 0.05545 0.04441 0.04073 0.02972 0.02065
## Cumulative Proportion  0.86449 0.90890 0.94963 0.97935 1.00000

umap_100 <- perform_umap(data_clean, 'bwt_100')
umap_100

##             [,1]         [,2]
## 2   -0.214306448 -3.947785635
## 4   -0.705589452 -4.441633588
## 5    2.065682762  3.665941153
## 7   -0.021561143 -3.656894425
## 10   0.475438934  1.000447931
## 11   0.860888101 -2.341927967
## 13   2.191097786 -0.998849987
## 14   0.800645085  1.288005869
## 15   2.148079283  2.464043331
## 16   2.388010149  4.037636992
## 17   0.360129017  0.123260007
## 19   0.592838348 -2.323767641
## 20  -0.083525761 -3.669438398
## 21   2.034261590  2.641907666
## 22   2.254217934 -1.014397878
## 23   3.965507992 -0.263656663
## 25   1.071496974 -3.055047031
## 27   2.437017582  3.871807913
## 28   2.306989765  3.980654619
## 29   1.049063783 -1.610519849
## 30   1.031054648 -3.130462581
## 31   2.116806497  2.596123450
## 32   2.274015447  4.019923087
## 35  -0.582856370 -4.193875425
## 36   0.538307397  0.872321928
## 40   2.477104410  3.866829595
## 41  -0.636625543 -4.281986894
## 42   0.780062270 -2.930520322
## 43  -0.160630950 -3.757898327
## 45   2.063650452  2.462526870
## 46   2.383588416 -0.775852878
## 47  -0.811333702 -4.470322275
## 48  -0.824132057 -4.473601044
## 50   2.222707652 -0.953474177
## 51   0.032850405 -3.102781153
## 53   1.240398192 -2.073294040
## 54   2.082354946  2.882833699
## 55   3.893814086 -0.618568384
## 56   0.575673704 -2.250553234
## 57   2.078373460  2.395926401
## 58  -0.178980507 -3.817869531
## 59   1.741721099 -1.752870193
## 62   0.896596237 -1.991448422
## 65   2.026821970  2.480630425
## 66   2.727159075 -0.731749520
## 67   2.433603374  3.781573795
## 68   0.896515036 -2.339736776
## 69   0.932694135 -2.641134668
## 70   2.328699755 -0.788689255
## 72  -0.653637313 -4.276119200
## 74  -1.254082147 -3.731624036
## 75   0.872144735 -2.603486928
## 76   0.895981949  1.569625441
## 77   2.246869273  3.866366088
## 78   3.793191982 -0.087809291
## 80   0.811920798 -2.209387406
## 81  -0.644857587 -4.387363115
## 82   2.130480208  2.505598244
## 83   0.480289398 -3.259280397
## 84   2.289336313  3.578949442
## 85   0.885933662 -2.645213337
## 86  -0.258930995 -3.881546405
## 87   1.749771654 -1.679183056
## 88   2.156109069  4.071752665
## 91   0.938470285 -3.157549693
## 92   0.868277029 -2.615310668
## 94   4.268842686 -0.791577341
## 95   1.033846795 -1.902528276
## 97   0.577624401  1.036507429
## 98   0.414822187 -2.324097339
## 99   0.849801699 -3.055857981
## 101  3.593619107 -0.442591731
## 102  0.886666276 -2.612839149
## 103  3.807523570 -0.183248752
## 104 -0.745978232 -4.326193992
## 105 -0.615315087 -4.235692809
## 107  1.735744592 -1.707382466
## 108  0.384499638  0.454555075
## 109  0.566462374 -2.310412263
## 111  2.122058268 -0.867024357
## 114  2.358413148  3.732244693
## 115 -0.462879338 -3.497688317
## 116 -0.269409350 -3.159469229
## 117  2.006478106  3.632809303
## 118  0.772287673 -2.739440483
## 119  1.960310659 -1.259868930
## 120  0.952308285 -2.288443248
## 121  2.135820066 -0.865911487
## 122 -0.643416803 -4.188203371
## 124 -0.360922913 -3.801354853
## 125  1.992684564  2.586894829
## 126  1.984389102  2.491866566
## 127  0.645386507 -2.145903440
## 128  1.765512054 -1.414516732
## 129  0.648414089 -3.083700057
## 130  2.283769231 -0.271632026
## 131  2.200777746  4.281645328
## 132  2.150554340 -0.744405522
## 133  2.233909229  3.869667797
## 134  1.983768987 -1.177789816
## 137  1.085854090 -3.180150660
## 139  0.473378674  1.031927623
## 140  1.870795779  3.070388348
## 141  3.851850224 -0.143060236
## 143 -0.827331918 -4.212724954
## 144 -0.886416193 -4.255873643
## 145  1.862567132  4.179337110
## 146  2.292555166 -0.048303248
## 148  1.759283036  2.727074066
## 149  0.285509600  0.296318167
## 150  2.617129050 -0.121020151
## 151  4.420174529 -0.717882478
## 152  0.048650845 -3.470892467
## 153  1.665390236 -1.495598235
## 154  0.823178963  1.215134615
## 155 -0.666341774 -3.931224822
## 156  1.692739799 -1.459961068
## 157  1.847265823 -1.289895038
## 159  0.006512767 -3.123811721
## 160  2.328119560 -0.793869355
## 161  1.818099102  2.427330223
## 162  2.156722255  3.616004972
## 163  1.886436083  2.455796872
## 164  1.874598714 -0.927268236
## 165  0.619873436 -2.837476866
## 166  1.706008326 -1.396267734
## 167  2.110773888 -0.683913176
## 168 -0.580930475 -3.515513350
## 169 -0.367031752 -3.505829439
## 170  1.826532077  2.181935657
## 172  2.256501995  3.735372174
## 173  1.484805483 -0.969487075
## 174  1.229283770  1.578782910
## 176  1.149521082  1.644977212
## 177  1.252644415 -2.101793058
## 179  2.220309126 -0.030600897
## 180  1.715424712  2.804093423
## 182  2.243394150 -0.030152223
## 183  1.928419142  4.304222884
## 184  1.938224836 -0.287211659
## 185  0.952004923  1.267040156
## 186 -0.262756461 -1.953398451
## 187  1.190475301  1.566503536
## 188  1.036502313 -3.228982970
## 189  3.991121024 -0.129181586
## 190 -1.252542655 -4.150265676
## 191  1.112764293 -3.221508413
## 192  2.155476227  4.260164670
## 193  0.002651700  1.392077863
## 194  1.845537818  3.795498256
## 195  2.104171274  3.745286086
## 196 -0.403410673 -1.822335836
## 197  0.348296145  0.701114017
## 198  0.328196880 -1.070689533
## 199  1.651273059 -0.882613390
## 201 -1.063489976 -3.477558822
## 202 -0.044601339 -0.513006540
## 203  4.709022297 -0.781997970
## 205 -0.776473126 -3.321721996
## 206  1.574149247  3.394190022
## 207 -0.179007875 -3.583262287
## 208  1.580603543 -1.393952346
## 210 -0.398471164 -1.827195393
## 211  1.812630470 -0.760803970
## 212 -0.711295809 -3.071853996
## 213  1.868037533  4.153576602
## 215  0.875029165  1.593847139
## 216  1.037378465  1.362739870
## 217  1.602852122  3.937400912
## 218  3.884879715 -0.218854214
## 219  0.246165782  0.655053965
## 220  0.956454688 -3.268511440
## 221  2.062025804  0.319613349
## 222 -0.039735829  1.229840368
## 223 -0.272715346 -1.405790035
## 224  4.673029854 -0.401037986
## 225 -1.366276634 -3.606942203
## 226  1.636625716  3.653826809
## 227  1.271284017  2.855354682
## 228 -0.273641089 -1.390118259
## 229  2.195282578 -0.020771290
## 230 -0.198979478 -0.119364858
## 231 -2.234507747 -4.121408079
## 232 -0.003056894  0.183418145
## 233 -2.261557119 -4.140513119
## 234  1.963512248  4.285448436
## 235 -0.641793859 -1.746294440
## 236  1.182485643  1.672893979
## 237  2.166752505 -0.065788125
## 238  1.951426165  4.600594752
## 239  1.525252303  3.931906790
## 240  1.700768733  4.091794858
## 241  1.060996677  2.759914749
## 242  0.323240140 -1.156582936
## 243 -0.010942247  0.082423352
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## 245  2.098834368  5.912447354
## 246 -1.418857255 -3.579386133
## 247  1.891185704  5.038633461
## 248  2.255957831 -0.060875769
## 249  1.444554629  3.791232952
## 250 -1.324906144 -3.384992687
## 251  0.816030493  2.745139249
## 253 -1.574136910 -3.405777450
## 255  0.087089399  0.244729188
## 256 -1.558397247 -3.565811875
## 257 -2.449902593 -4.023999781
## 259 -0.255850864  0.032020267
## 260 -0.249394838 -0.209050062
## 261  4.611087109 -0.642803489
## 262 -2.289925454 -4.093304507
## 263  0.689343535 -1.090696612
## 264 -0.909156032 -2.781197983
## 265 -2.158103905 -4.028679455
## 267 -0.079896836  0.117759094
## 268 -0.580100703 -1.468130573
## 269 -1.425683791 -3.231711867
## 270  1.470497995  4.071567397
## 271  1.040116343  1.104929838
## 272  0.886200441 -1.071244953
## 273 -0.205449215 -1.258048800
## 274 -1.120274275 -2.306168566
## 275 -0.079545861  1.329500070
## 276  4.584353483 -0.707691882
## 277  1.400153551  4.045123382
## 278 -0.835297422 -1.756264307
## 279  1.863419278  4.958973999
## 280 -2.358847759 -1.597963067
## 281 -1.130103781 -2.231070171
## 282 -0.779059210 -1.699792249
## 284 -0.196503983 -0.255289316
## 285  0.346458673  1.600734856
## 286 -2.788388565 -4.087548325
## 287  0.522335735  3.065031735
## 288 -0.326849417 -0.193087027
## 289 -1.424355955 -2.883495402
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## 295  0.440905012 -1.035526436
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## 297  4.636858717 -1.042746740
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## 300 -0.274062252  1.287284630
## 301  4.516914891 -1.057465337
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## 304  5.023556746 -0.702219634
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## 307 -2.127585016 -3.681293531
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## 315 -0.642115915 -1.305946249
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## 356  4.309902118 -1.236854622
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## 358  0.938091029  4.230593699
## 360  0.762539142  3.939069284
## 361 -1.076281093 -1.717974796
## 362 -1.838869627 -3.395126674
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## 531 -0.853195597  3.120148423
## 532 -1.508387317  2.488313879
## 533  1.460237004  5.767878047
## 534 -4.051010683 -1.732134851
## 535 -4.068629797 -1.730420233
## 536 -2.747577651  0.400910505
## 537 -3.990444528 -3.232706331
## 538 -2.566045693  0.537479293
## 539 -2.460850039 -1.181367490
## 541  5.344758317 -0.334988292
## 542 -2.817575423  0.045878872
## 543  5.305310625 -0.181347731
## 545 -2.500003613 -0.045723136
## 546 -4.125019269 -1.858035732
## 547 -3.571002667 -0.827895449
## 548  5.382484442  0.181977491
## 550 -0.706852844  1.759080549
## 551 -3.941890537 -1.409549722
## 555  1.465040092  6.062424559
## 558 -4.050702863 -1.727746104
## 560 -0.774044876  3.489556608
## 561 -2.860435987  0.055983847
## 563 -0.740785384  0.883309145
## 564  1.384387399  6.135068645
## 566 -0.960839330  3.299793335
## 568  1.323212219  5.931017006
## 569 -1.259105161  3.115989591
## 571 -3.898841157 -1.278869597
## 572 -4.061875688 -3.259240515
## 573 -3.743169033 -1.339556830
## 574  5.218865018 -0.295996546
## 575 -3.883312099 -1.406038615
## 578 -3.219451447 -0.196612277
## 579 -3.520085799 -0.633090220
## 580 -2.238946123 -0.827380285
## 581 -1.222326060  3.196859380
## 583 -0.908763872  3.393027817
## 584 -1.042304567  2.512471134
## 585 -3.585851053 -4.050874795
## 586 -3.908053556 -1.424969210
## 587 -4.208378119 -1.739543586
## 588 -2.641932771  0.468835782
## 590 -3.994389464 -3.397830185
## 591 -0.623076932  1.208027077
## 592 -3.464693199 -0.714042367
## 593 -1.046500764  2.665309073
## 594  1.366762826  5.593223154
## 597 -2.616767710  0.600349486
## 599 -4.054337880 -3.252529784
## 600  1.639964718  6.115483041
## 601  5.427883821 -0.034709392
## 602 -0.544676073  1.360776298
## 603 -0.828545458  0.759635976
## 604 -4.031626128 -3.338221462
## 605 -1.419722695  2.736873259
## 606 -4.165448144 -1.524353522
## 608 -2.379034606 -0.576733494
## 609 -4.011018773 -1.084770221
## 610 -1.001451030  3.107237691
## 611 -2.735467929  0.094302944
## 613 -1.235166845  3.143898102
## 615 -1.415354222  2.613766921
## 616 -4.204863272 -1.297427162
## 619  1.859559495  6.180238058
## 620  1.469478130  5.852607376
## 622 -4.255379481 -1.681390783
## 623 -4.208045098 -1.679792848
## 624 -4.142524915 -1.140932524
## 625 -3.373814425 -0.327632315
## 626 -2.220436631 -0.747090103
## 628 -2.853505605  0.395351564
## 629 -4.196600253 -2.414088893
## 630 -3.520905729 -0.522501110
## 631 -4.163493225 -1.180841584
## 632 -1.059777512  2.375832027
## 634 -1.326001843  2.557253261
## 636 -2.976575324 -0.018718898
## 638  1.317806826  6.175886657
## 641 -2.329360497 -0.547616796
## 642 -4.115134235 -3.229364958
## 643  1.292088115  6.175836194
## 647  1.602890188  6.134915844
## 648 -2.287530741 -0.794629350
## 649 -3.557470457 -0.514787309
## 650 -2.932287940  0.276550466
## 652  1.203740883  6.216805284
## 661 -4.243507620 -2.188620616
## 662 -4.326298325 -1.550611249
## 664 -1.326971418  2.909469671
## 666 -4.172265632 -1.108485538
## 667  1.207864897  6.131586720
## 671 -1.374800263  3.110835365

ggplot(data.frame(PC1 = pca_original$x[,1], PC2 = pca_original$x[,2]), aes(x = PC1, y = PC2)) + 
  geom_point() + ggtitle("PCA - O")

ggplot(data.frame(PC1 = pca_50$x[,1], PC2 = pca_50$x[,2]), aes(x = PC1, y = PC2)) + 
  geom_point() + ggtitle("PCA - 50% ")

ggplot(data.frame(PC1 = pca_100$x[,1], PC2 = pca_100$x[,2]), aes(x = PC1, y = PC2)) + 
  geom_point() + ggtitle("PCA - 100% ")

ggplot(data.frame(UMAP1 = umap_original[,1], UMAP2 = umap_original[,2]), aes(x = UMAP1, y = UMAP2)) + 
  geom_point() + ggtitle("UMAP - Orig")

ggplot(data.frame(UMAP1 = umap_50[,1], UMAP2 = umap_50[,2]), aes(x = UMAP1, y = UMAP2)) + 
  geom_point() + ggtitle("UMAP - 50% ")

ggplot(data.frame(UMAP1 = umap_100[,1], UMAP2 = umap_100[,2]), aes(x = UMAP1, y = UMAP2)) + 
  geom_point() + ggtitle("UMAP - 100% ")

Честно говоря я не понимаю, что происходит, по визуализации как будто кумулятивная не должна меняться, просто новые кластеры появляются, но общий результат должен быть похожим

Если вам не трудно, могли бы вы в фидбеке обьяснить, как правильно интерпретировать и как делать последние два пункта :) Я сдаюсь…